Finding the sum of an infinite series can be really tricky. Here are some challenges you might run into:

1. Convergence Issues: Not all series add up nicely. Some do not come to a limit, which means they don’t have a meaningful sum.

2. Complex Formulas: The math formulas used to calculate sums can be complicated and hard to remember.

3. Special Cases: Some series, like geometric series, have certain rules that must be followed to find their sums.

But don’t worry! There are different ways to solve these issues:

• Geometric Series: If you have a geometric series with a first term called $a$ and a common ratio $r$ (where $|r| < 1$), you can find the sum using the formula $\frac{a}{1 - r}$.

• Test for Convergence: Before finding a sum, you can use tests like the ratio test or the root test to see if the series converges or adds up properly.

With these methods, you can tackle those challenges and find the sums you're looking for!